I do believe it is property laws and trust law and other civil law that will be the subject of the court’s jurisdiction not the religious teachings of the Presbyterian Church. How those questions of civil law are decided usually does hinge on the internal heirarchal structure of the church. Which can be very confusing to many judges if the recent TEC cases are any indication.
You are correct - property is at the heart of the civil cases. However, the “rules and regulations” of the Presbyterian Church (USA) will need to be considered by the civil courts when rendering the decisions.